(CNN) -- Voters in Washington state and Wyoming hold primaries Tuesday, with the Senate contest in Washington and a battle for the open Wyoming governor's seat the most closely watched races of the day.

In Washington, Democratic Sen. Patty Murray and Republican candidate Dino Rossi are expected to emerge from a crowded primary field, setting up a November showdown. Under the state's system, the two candidates who receive the most votes regardless of party affiliation move on to the general election. Voting has been underway for two weeks, with Washington primarily a mail-in ballot state.

In many ways, Murray and Rossi have already begun their general election campaigns, focusing their attacks on each other. Polls show a close race in the fall if they both advance.

Nathan Gonzales, political editor of the Rothenberg Political Report, said the system gives "a sneak preview of what a head-to-head race (in the fall) will look like." But he cautions that analysts "should pause before drawing too many conclusions" on what the numbers from a primary race say about November.

For Rossi, this is the third run for statewide office in the last six years after twice losing close races for governor to Democrat Christine Gregoire. "Rossi's past cuts both ways," Gonzales said. "It gives him name recognition that can be expensive to get, but brings some of the dirty laundry that's been aired in the past races."

Among Republicans also running are conservatives Paul Akers and former NFL tight end Clint Didier. Didier has the backing of former Alaska Gov. Sarah Palin, who has recorded a robocall on his behalf. The Seattle Times reports Palin said in the call that "unlike establishment candidates who just talk about lower taxes, Clint has signed a pledge to do so."

Murray is seeking a fourth term in the Senate and, as in her two previous re-election bids, she is a target of national Republicans. The Rothenberg Political Report rates the race a toss-up/tilt Democrat in the fall, but Gonzales said Republicans are optimistic they can change the outcome.

"It's all about the cycle," Gonzales said. "A majority of Americans are dissatisfied and looking for change. This is a year to tap in, in places like the Northwest where's it been difficult in recent years."

President Barack Obama was in Seattle, Washington, on Tuesday appearing at a fundraiser for Murray. "Murray understands she's a target," said Gonzales, who added that the fundraiser is about getting "resources necessary to get her message out."

While some Democrats have chosen not to appear alongside Obama, Gonzales noted that, "Republicans will try to tie Murray to Obama no matter what she does, so she might as well have the money to defend herself."

The Washington secretary of state is predicting a 38 percent turnout in the primary, with voters allowed to drop off ballots until 8 p.m. PT on Tuesday.

In Wyoming, Republicans are hoping to reclaim the governor's mansion as Democrat Dave Freudenthal leaves office. Seven Republicans are competing for the GOP nomination, while five Democrats are running for their party's nod.

A Mason-Dixon poll conducted three weeks before the election for the Casper Star-Tribune showed that in the race for the GOP nomination, State Auditor Rita Meyer led former U.S. Attorney Matt Mead by a 27 percent to 24 percent margin, but her lead was inside the margin of error. Colin Simpson, son of former U.S. Sen. Alan Simpson, received 17 percent in the same GOP survey, while Ron Micheli polled at 12 percent.

Meyer received the backing of Palin in the final weeks of the campaign, with the former Alaska governor writing on her Facebook page, "her true grit has not escaped the eye of other Americans who know that at every level of political office we all benefit with commonsense constitutional conservatives in service."

The Mason-Dixon poll showed Leslie Peterson leading Peter Gosar 30 percent to 22 percent in the battle for the Democratic nomination. Three other candidates polled at 2 percent or less.